Class 12 Probability · Long Answer3 Marksprobability_distributions

Class 12 Maths · Probability · Long Answer #111

A group has50 scouts,30 trained in first aid and20 not. Select2 uniformly without replacement. Find the distribution and mean of the number trained in first aid.

✅ Step-by-Step Solution

Final Answer: P(X=0)=38/245; P(X=1)=24/49; P(X=2)=87/245. Mean=6/5.

Let X count the designated type in a uniform sample of 2 drawn without replacement from 50 items, 30 of the designated type.
There are C(50,2)=1225 equally likely samples. For admissible k, P(X=k)=C(30,k)C(20,2−k)/C(50,2). The probabilities are P(X=0)=38/245; P(X=1)=24/49; P(X=2)=87/245. Their sum is 1.
E(X)=ΣxP(X=x)=(0)(38/245)+(1)(24/49)+(2)(87/245)=6/5.
P(X=0)=38/245; P(X=1)=24/49; P(X=2)=87/245. Mean=6/5.

📋 CBSE Stepwise Marking Scheme

[0.5 marks] Let X count the designated type in a uniform sample of 2 drawn without replacement from 50 items, 30 of the designated type.
[1 mark] There are C(50,2)=1225 equally likely samples. For admissible k, P(X=k)=C(30,k)C(20,2−k)/C(50,2). The probabilities are P(X=0)=38/245; P(X=1)=24/49; P(X=2)=87/245. Their sum is 1.
[1 mark] E(X)=ΣxP(X=x)=(0)(38/245)+(1)(24/49)+(2)(87/245)=6/5.
[0.5 marks] P(X=0)=38/245; P(X=1)=24/49; P(X=2)=87/245. Mean=6/5.

Master Chapter 13: Probability

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Probability.

📘 Chapter Notes & All Exercises 🚀 Open Interactive Workspace →

← Previous Question

X is the number of colleges granting admission to an applicant. Its…

Next Question →

In a school,30% have full attendance and70% are irregular. Grade A…

Class 12 Maths · Probability · Long Answer #111

✅ Step-by-Step Solution

📋 CBSE Stepwise Marking Scheme

Master Chapter 13: Probability

More Practice Questions in Probability

Related Questions in Probability